the easiest way to catch Feebas is to trade for one with someone who actually found it. Thats what I did.... Most people are nice enough that if they find/catch Feebas to breed them trade with others.
On a side note, even though I traded for my first Feebas, I found him myself on a fluke. I was fishing for Carvanah for AT EV training, and stumbled into a Feebas spot....
To catch your own Feebas, try each and every square, start either at top or bottem and just work your way down, searching like 4-6 times in each spot. Not easy, but its the easiest way